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Prime Perimeter (Posted on 2005-03-11) Difficulty: 3 of 5

You and two other people have numbers written on your foreheads. You are all told that the three numbers are primes and that they form the sides of a triangle with a prime perimeter. You see 5 and 7 on the other two heads and both of the other people agree that they cannot deduce the number on their own foreheads.

What is the number written on your forehead?

  Submitted by Erik O.    
Rating: 2.8235 (17 votes)
Solution: (Hide)

1 - The three possibilities are that you have 5, 7, or 11 on your forehead.

2 - If you have a 5, then person A, with 7, sees (5, 5) and concludes that he must have a 3 or 7, but if he has 3 then he reasons that person B sees (5, 3) and would know his number is 5 or 3. B can eliminate 3 because anyone seeing (3, 3) would immediately know he had 5. Since B doesn't know his number, A would conclude that he has 7. Since A doesn't draw this conclusion you know you don't have a 5.

3 - If you have a 7 then person B with a 5 sees (7, 7) and concludes he has 3 or 5, but if he has 3 then he erasons that person A, with 7, sees (7, 3) and would know know his number is 7. Since A doesn't know his number, then B would conclude he has a 5. Since B doesn't draw this conclusion, you know you don't have a 7.

Therefore you have 11 on your forehead.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
answerK Sengupta2007-03-14 04:06:06
re: SolutionJacob2005-05-20 21:02:28
re: Solution (to Briana)pcbouhid2005-04-25 21:12:13
SolutionSolutionBriana2005-04-23 02:35:31
too simpleravikumar2005-04-22 04:44:33
SolutionSolution (long)Eddy Karat2005-04-13 22:08:34
re(2): full solutionSue Levy2005-04-10 16:41:45
re(3): THERE IS NO SOLUTION!Dustin2005-04-09 02:55:50
re(2): THERE IS NO SOLUTION!jon2005-04-09 01:30:25
re: THERE IS NO SOLUTION!Dustin2005-04-09 00:44:59
SolutionTHERE IS NO SOLUTION!jon2005-04-09 00:11:17
THERE IS NO SOLUTION!jon2005-04-09 00:11:11
Some Thoughtsre(2): A solution to Patjon2005-04-08 23:28:55
re: No Subject - To Samarapcbouhid2005-04-05 18:54:32
No SubjectSamara2005-04-05 17:21:49
re: A solution to Patpcbouhid2005-04-05 16:07:25
SolutionA solutionPat Whitaker2005-04-05 01:34:25
to jason, why your answer is wrongMichael2005-04-04 12:00:27
re: prime perimetergary wallravin2005-03-27 20:01:44
re: prime perimeter - To Jasonpcbouhid2005-03-27 13:22:06
re: prime perimeterpcbouhid2005-03-26 21:07:59
Solutionprime perimeterjason2005-03-26 02:58:33
re: Prime Perimetergary wallravin2005-03-22 18:58:22
re(2): solutiongary wallravin2005-03-22 18:51:04
Prime PerimeterBrunner, J2005-03-22 14:51:23
No Subjectdavid2005-03-22 13:16:18
Some Thoughtstrying to solveChandraKumar Desai2005-03-21 05:45:58
re: solutionem2005-03-21 02:20:42
Solutionsolutiongary wallravin2005-03-20 20:44:31
No Subjectrachael2005-03-18 02:56:18
re: No Subject (emdad)pcbouhid2005-03-16 12:25:49
No Subjectemdad2005-03-16 10:25:39
re(3): centering the pointpcbouhid2005-03-15 15:49:59
re: No Subjectpcbouhid2005-03-15 15:25:03
solutionnitin2005-03-15 07:53:11
No Subjectemdad2005-03-14 22:04:02
re(2): centering the pointarmando2005-03-14 21:46:09
No Subjectemdad2005-03-14 21:37:39
re(2): 5,5,9--7,7,9--7,7,13john2005-03-14 17:42:51
re(6): Trying to solve this...pcbouhid2005-03-14 17:02:24
re: 5,5,9--7,7,9--7,7,13pcbouhid2005-03-14 16:57:33
re(5): Trying to solve this...pcbouhid2005-03-14 16:53:47
unique?john2005-03-14 15:35:08
5,5,9--7,7,9--7,7,13john2005-03-14 15:24:47
re: full solutionjohn2005-03-14 15:04:18
re: solution?john2005-03-14 14:38:55
re(4): Trying to solve this...Tristan2005-03-14 00:50:01
re: centering the pointpcbouhid2005-03-13 23:30:06
re(3): Trying to solve this...pcbouhid2005-03-13 23:22:34
re(2): Trying to solve this...Tristan2005-03-13 22:06:15
re: Trying to solve this...pcbouhid2005-03-13 21:07:54
re: centering the pointpcbouhid2005-03-13 20:54:36
centering the pointarmando2005-03-13 09:56:43
Questionre: Erick Please ClarifyTristan2005-03-13 02:10:23
Some ThoughtsTrying to solve this...Tristan2005-03-13 01:50:45
solutionKyle Mooney2005-03-12 18:17:03
re(2): Charlie's SkepticismEric2005-03-12 17:00:06
re: Charlie's SkepticismCharlie2005-03-12 14:09:04
Solutionre(2): still another wordRex2005-03-12 07:58:33
Solutionre: one word moreRex2005-03-12 07:57:33
Solutionone wordRex2005-03-12 07:55:20
Charlie's SkepticismEric2005-03-12 05:23:59
Erick Please ClarifySachin2005-03-12 05:12:38
re(4): full solution as understoodSachin2005-03-12 05:10:38
re(3): full solution as understoodSachin2005-03-12 04:11:29
re: No SubjectDonna2005-03-12 03:35:14
No Subjectjenny2005-03-12 03:32:20
re(3): full solution as understoodSachin2005-03-12 03:06:51
re(2): full solution as understoodCharlie2005-03-12 03:01:36
re: full solution as understoodSachin2005-03-12 02:00:00
solutionDanielle2005-03-12 01:31:25
Triangles and Primes -Gordon Steel2005-03-12 00:56:14
re: full solutionSachin2005-03-11 23:18:29
re: full solutionMike2005-03-11 22:41:05
re(3): full solution - to Hugo againpcbouhid2005-03-11 21:55:26
re(2): full solution - to Hugo againpcbouhid2005-03-11 21:52:53
re(2): full solution - To Hugopcbouhid2005-03-11 21:48:53
re(2): full solutionpcbouhid2005-03-11 21:44:45
re: full solutionHugo2005-03-11 21:41:05
re: full solutionMike2005-03-11 21:09:50
re(2): full solutionpcbouhid2005-03-11 21:02:34
re: full solutionCharlie2005-03-11 20:35:47
Solutionfull solutionpcbouhid2005-03-11 19:27:14
re(3): Semi-Solution?Sachin2005-03-11 19:17:15
re(2): Semi-Solution?Richard2005-03-11 19:14:59
So far ....Sachin2005-03-11 18:54:47
re: Semi-Solution?Charlie2005-03-11 18:26:51
Semi-Solution?lauren2005-03-11 17:42:13
solution?john2005-03-11 17:28:25
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